{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Centroid measurement\n",
    "\n",
    "Author: Charles Le Losq\n",
    "\n",
    "This notebook illustrates the use of the `rampy.centroid()` function to measure the centroid of a peak."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/charles/miniconda3/envs/py36/lib/python3.6/site-packages/sklearn/ensemble/weight_boosting.py:29: DeprecationWarning: numpy.core.umath_tests is an internal NumPy module and should not be imported. It will be removed in a future NumPy release.\n",
      "  from numpy.core.umath_tests import inner1d\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "np.random.seed(42) # fixing the seed\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import rampy as rp\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem definition\n",
    "\n",
    "The rampy.centroid function will calculate the centroid of the signal you provide to it.\n",
    "\n",
    "In this case, we have a combination of two Gaussian peaks with some noise. This example is that used in the Machine Learning Regression notebook.\n",
    "\n",
    "The example signals $D_{i,j}$ are generated from a linear combination of two Gaussian peaks $S_{k,j}$, and are affected by a constant background $\\epsilon_{i,j}$:\n",
    "\n",
    "$$ D_{i,j} = C_{i,k} \\times S_{k,j} + \\epsilon_{i,j}$$\n",
    "\n",
    "We thus will remove the background, then calculate the centroid, and plot it against $C_{i,k}$ which is known in the present case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of samples:100\n",
      "Shape of partial spectra matrix:(2, 600)\n",
      "Shape of concentration matrix:(100, 2)\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(0,600,1.0)\n",
    "nb_samples = 100 # number of samples in our dataset\n",
    "\n",
    "# partial spectra\n",
    "S_1 = scipy.stats.norm.pdf(x,loc=300.,scale=40.)\n",
    "S_2 = scipy.stats.norm.pdf(x,loc=400,scale=20)\n",
    "S_true = np.vstack((S_1,S_2))\n",
    "print(\"Number of samples:\"+str(nb_samples))\n",
    "print(\"Shape of partial spectra matrix:\"+str(S_true.shape))\n",
    "\n",
    "# concentrations\n",
    "C_ = np.random.rand(nb_samples) #60 samples with random concentrations between 0 and 1\n",
    "C_true = np.vstack((C_,(1-C_))).T\n",
    "print(\"Shape of concentration matrix:\"+str(C_true.shape))\n",
    "\n",
    "# background\n",
    "E_ = 1e-8*x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "true_sig = np.dot(C_true,S_true)\n",
    "Obs = np.dot(C_true,S_true) + E_ + np.random.randn(nb_samples,len(x))*1e-4\n",
    "\n",
    "# norm is a class which, when called, can normalize data into the\n",
    "# [0.0, 1.0] interval.\n",
    "norm = matplotlib.colors.Normalize(\n",
    "    vmin=np.min(C_),\n",
    "    vmax=np.max(C_))\n",
    "\n",
    "# choose a colormap\n",
    "c_m = matplotlib.cm.jet\n",
    "\n",
    "# create a ScalarMappable and initialize a data structure\n",
    "s_m = matplotlib.cm.ScalarMappable(cmap=c_m, norm=norm)\n",
    "s_m.set_array([])\n",
    "\n",
    "# plotting spectra\n",
    "# calling the ScalarMappable that was initialised with c_m and norm\n",
    "for i in range(C_.shape[0]):\n",
    "    plt.plot(x,\n",
    "             Obs[i,:].T,\n",
    "             color=s_m.to_rgba(C_[i]))\n",
    "\n",
    "# we plot the colorbar, using again our\n",
    "# ScalarMappable\n",
    "c_bar = plt.colorbar(s_m)\n",
    "c_bar.set_label(r\"C_\")\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Baseline fit\n",
    "\n",
    "We will use the rampy.baseline function with a polynomial form.\n",
    "\n",
    "We first create the array to store baseline-corrected spectra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 600)\n"
     ]
    }
   ],
   "source": [
    "Obs_corr = np.ones(Obs.shape)\n",
    "print(Obs_corr.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define regions of interest ROI where the baseline will fit the signals. From the previous figure, this is clear that it should be between 0 and 100, and 500 and 600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0. 100.]\n",
      " [500. 600.]]\n"
     ]
    }
   ],
   "source": [
    "ROI = np.array([[0.,100.],[500.,600.]])\n",
    "print(ROI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we loop to save the baseline corrected data in this array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(nb_samples):\n",
    "    sig_corr, bas_, = rp.baseline(x,Obs[i,:].T,ROI,method=\"poly\",polynomial_order=2)\n",
    "    Obs_corr[i,:] = sig_corr.reshape(1,-1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting spectra\n",
    "# calling the ScalarMappable that was initialised with c_m and norm\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(1,2,1)\n",
    "\n",
    "for i in range(C_.shape[0]):\n",
    "    plt.plot(x,\n",
    "             Obs[i,:].T,\n",
    "             color=s_m.to_rgba(C_[i]), alpha=0.3)\n",
    "\n",
    "plt.plot(x,bas_,\"k-\",linewidth=4.0,label=\"baseline\")\n",
    "\n",
    "# we plot the colorbar, using again our\n",
    "# ScalarMappable\n",
    "c_bar = plt.colorbar(s_m)\n",
    "c_bar.set_label(r\"C_\")\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.legend()\n",
    "plt.title(\"A) Baseline fit\")\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "\n",
    "for i in range(C_.shape[0]):\n",
    "    plt.plot(x,\n",
    "             Obs_corr[i,:].T,\n",
    "             color=s_m.to_rgba(C_[i]), alpha=0.3)\n",
    "\n",
    "\n",
    "c_bar = plt.colorbar(s_m)\n",
    "c_bar.set_label(r\"C_\")\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title(\"B) Corrected spectra\")\n",
    "plt.show()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Centroid determination"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can calculate the centroid of the signal. rampy.centroid calculates it as\n",
    "\n",
    "`centroid = np.sum(y_/np.sum(y_)*x)`\n",
    "\n",
    "It accepts arrays of spectrum, organised as n points by m samples.\n",
    "\n",
    "Smoothing can be done if wanted, by indicating `smoothing = True`. We will compare both in the following code.\n",
    "\n",
    "A tweak is to prepare an array fo x with the same shape as y, and the good x values in each columns.\n",
    "\n",
    "Furthermore, do not forget that arrays should be provided as n points by m samples. So use `.T` if needed to transpose your array. We need it below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_array = np.ones((len(x),nb_samples))\n",
    "for i in range(nb_samples):\n",
    "    x_array[:,i] = x\n",
    "\n",
    "centroids_no_smooth = rp.centroid(x_array,Obs_corr.T)\n",
    "centroids_smooth = rp.centroid(x_array,Obs_corr.T,smoothing=True)\n",
    "centroids_true_sig = rp.centroid(x_array,true_sig.T,smoothing=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the centroids against the chemical ratio C_ for instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f89317d1668>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(C_,centroids_true_sig,\"r-\",markersize=3.,label=\"true values\")\n",
    "plt.plot(C_,centroids_no_smooth,\"k.\",markersize=5., label=\"non-smoothed centroids\")\n",
    "plt.plot(C_,centroids_smooth,\"b+\",markersize=3., label=\"smoothed centroids\")\n",
    "plt.xlabel(\"Fraction C_\")\n",
    "plt.ylabel(\"Signal centroid\")\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
